texture painting one object also paints another & vise versa
I'll ignore the symmetry you have active for now, as the UV problem i see should not be affected by it. Still, symmetry while painting on bad UV's can give headaches too, but more to that below.

From the picture, which is all i have to base my answer on, it looks like the UV's of all objects are on the same texture (one material for the entire X-Wing) and while they are unwrapped, not all faces belonging to a surface are together in islands. Some faces seem to be switched around. It's not possible to see in this picture, but i would guess that some of the UV's may be lying on top of each other and thus painting there paints on the underlying UV's, thus the object it belongs to as well.

I would suggest make a backup of the file and then generate new UV's, be it by doing it from the scratch, or by selecting already ok islands and moving them aside first to find the broken up ones and fixing them.

I'd go through the objects and select the surfaces in question, when the UV's show up highlighted, grab them and move them outside the texture frame, if you find UV's that are lying on top of another you found the problem. By re-positioning them so they do not overlap, you can fix the problem. Some UV's as i mentioned seem to be broken up and could be fixed as well. For that just select all the corresponding UV-faces and unwrap them again (you need to know how though, as UV unwrapping is a bit too much to explain here) You could try "Smart UV project", but mainly the overlapping UV's are to be re-positioned, as long as all UV's are packed anew and have some space around them, painting in the 3D-View should work fine. Having the faces of a surface in one island though makes for a cleaner picture and avoids some texturing problems in the long run.

Once all UV's are spread out and none are overlapping anymore, you can select them all and first "UV->Average Islands Scale" and then "UV->Pack Islands". That will bring the sizes of the UV's to an average in relation to the size of the faces on the object and then pack them on the texture frame.

Now you can paint to your hearts content.
Happy blending.